As part of an ongoing worldwide effort to comprehend and monitor insect biodiversity, this paper presents the BIOSCAN-5M Insect dataset to the machine learning community and establish several benchmark tasks. BIOSCAN-5M is a comprehensive dataset containing multi-modal information for over 5 million insect specimens, and it significantly expands existing image-based biological datasets by including taxonomic labels, raw nucleotide barcode sequences, assigned barcode index numbers, geographical, and size information. We propose three benchmark experiments to demonstrate the impact of the multi-modal data types on the classification and clustering accuracy. First, we pretrain a masked language model on the DNA barcode sequences of the BIOSCAN-5M dataset, and demonstrate the impact of using this large reference library on species- and genus-level classification performance. Second, we propose a zero-shot transfer learning task applied to images and DNA barcodes to cluster feature embeddings obtained from self-supervised learning, to investigate whether meaningful clusters can be derived from these representation embeddings. Third, we benchmark multi-modality by performing contrastive learning on DNA barcodes, image data, and taxonomic information. This yields a general shared embedding space enabling taxonomic classification using multiple types of information and modalities. The code repository of the BIOSCAN-5M Insect dataset is available at https://github.com/bioscan-ml/BIOSCAN-5M.

SUMMARY: We present an interactive Deep Learning-based software tool for Unsupervised Clustering of DNA Sequences (iDeLUCS), that detects genomic signatures and uses them to cluster DNA sequences, without the need for sequence alignment or taxonomic identifiers. iDeLUCS is scalable and user-friendly: its graphical user interface, with support for hardware acceleration, allows the practitioner to fine-tune the different hyper-parameters involved in the training process without requiring extensive knowledge of deep learning. The performance of iDeLUCS was evaluated on a diverse set of datasets: several real genomic datasets from organisms in kingdoms Animalia, Protista, Fungi, Bacteria, and Archaea, three datasets of viral genomes, a dataset of simulated metagenomic reads from microbial genomes, and multiple datasets of synthetic DNA sequences. The performance of iDeLUCS was compared to that of two classical clustering algorithms (k-means++ and GMM) and two clustering algorithms specialized in DNA sequences (MeShClust v3.0 and DeLUCS), using both intrinsic cluster evaluation metrics and external evaluation metrics. In terms of unsupervised clustering accuracy, iDeLUCS outperforms the two classical algorithms by an average of ∼20%, and the two specialized algorithms by an average of ∼12%, on the datasets of real DNA sequences analyzed. Overall, our results indicate that iDeLUCS is a robust clustering method suitable for the clustering of large and diverse datasets of unlabeled DNA sequences. AVAILABILITY AND IMPLEMENTATION: iDeLUCS is available at https://github.com/Kari-Genomics-Lab/iDeLUCS under the terms of the MIT licence.

SUMMARY: SomaticSiMu is an in silico simulator of single and double base substitutions, and single base insertions and deletions in an input genomic sequence to mimic mutational signatures. SomaticSiMu outputs simulated DNA sequences and mutational catalogues with imposed mutational signatures. The tool is the first mutational signature simulator featuring a graphical user interface, control of mutation rates and built-in visualization tools of the simulated mutations. Simulated datasets are useful as a ground truth to test the accuracy and sensitivity of DNA sequence classification tools and mutational signature extraction tools under different experimental scenarios. The reliability of SomaticSiMu was affirmed by (i) supervised machine learning classification of simulated sequences with different mutation types and burdens, and (ii) mutational signature extraction from simulated mutational catalogues. AVAILABILITY AND IMPLEMENTATION: SomaticSiMu is written in Python 3.8.3. The open-source code, documentation and tutorials are available at https://github.com/HillLab/SomaticSiMu under the terms of the CreativeCommonsAttribution4.0InternationalLicense. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

SUMMARY: Machine Learning with Digital Signal Processing and Graphical User Interface (MLDSP-GUI) is an open-source, alignment-free, ultrafast, computationally lightweight, and standalone software tool with an interactive GUI for comparison and analysis of DNA sequences. MLDSP-GUI is a general-purpose tool that can be used for a variety of applications such as taxonomic classification, disease classification, virus subtype classification, evolutionary analyses, among others. AVAILABILITY AND IMPLEMENTATION: MLDSP-GUI is open-source, cross-platform compatible, and is available under the terms of the Creative Commons Attribution 4.0 International license (http://creativecommons.org/licenses/by/4.0/). The executable and dataset files are available at https://sourceforge.net/projects/mldsp-gui/. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

In this paper we define and investigate a binary word operation that formalizes an experimentally observed outcome of DNA computations, performed to generate a small gene library, and implemented using a DNA recombination technique called Cross-pairing Polymerase Chain Reaction (XPCR). The word ble nding between two words αwγ1 and γ2wβ that share a non-empty overlap w, results in αwβ. Interestingly, this phenomenon has been observed independently in linguistics, under the name “blend word” or “portmanteau”, and is responsible for the creation of words in the English language such as smog (smoke + fog), labradoodle (labrador + poodle), and Brangelina (Brad + Angelina). Technically, word blending is related to the binary word operation Latin product, the crossover operation, and simple splicing. We study closure properties of the families in the Chomsky hierarchy under word blending, language equations involving this operation, and its descriptional state complexity when applied to regular languages. We also define iterated word blending and show that, for a given alphabet, there are finitely many languages that can be obtained from an initial language by iterated word blending.

SUMMARY: MoDMaps3D (Molecular Distance Maps 3D) is an alignment-free, fast, computationally lightweight webtool for computing and visualizing the interrelationships within any dataset of DNA sequences, based on pairwise comparisons between their oligomer compositions. MoDMaps3D is a general-purpose interactive webtool that is free of any requirements on sequence composition, position of the sequences in their respective genomes, presence or absence of similarity or homology, sequence length, or even sequence origin (biological or computer-generated). AVAILABILITY AND IMPLEMENTATION: MoDMaps3D is open source, cross-platform compatible, and is available under the MIT license at http://moleculardistancemaps.github.io/MoDMaps3D/. The source code is available at https://github.com/moleculardistancemaps/MoDMaps3D/. CONTACT: [email protected]. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

We propose the concept of self-assembly of smart tiles, i.e., tiles which possess a local computational device in addition to having edge glues that can be activated or deactivated by signals. The local tile computational device can range from its being absent, to being a counter, a simple look-up table, a finite state machine, all the way to being a Turing machine. Thus, this model offers a general framework to discuss and compare various tile self-assembly systems. We demonstrate the potential of self-assembly with smart tiles to efficiently perform robotic tasks such as the replication of convex shapes. The smart tile assembly system that we propose for convex shape replication does not make any assumption on the glues and signals of the interior tiles of the input supertile, and uses a scaffold to assemble a replica adjacent to the input supertile.

BACKGROUND: Studies exploring the potential of Chaos Game Representations (CGR) of genomic sequences to act as "genomic signatures" (to be species- and genome-specific) showed that CGR patterns of nuclear and organellar DNA sequences of the same organism can be very different. While the hypothesis that CGRs of mitochondrial DNA sequences can act as genomic signatures was validated for a snapshot of all sequenced mitochondrial genomes available in the NCBI GenBank sequence database, to our knowledge no such extensive analysis of CGRs of nuclear DNA sequences exists to date. RESULTS: We analyzed an extensive dataset, totalling 1.45 gigabase pairs, of nuclear/nucleoid genomic sequences (nDNA) from 42 different organisms, spanning all major kingdoms of life. Our computational experiments indicate that CGR signatures of nDNA of two different origins cannot always be differentiated, especially if they originate from closely-related species such as H. sapiens and P. troglodytes or E. coli and E. fergusonii. To address this issue, we propose the general concept of additive DNA signature of a set (collection) of DNA sequences. One particular instance, the composite DNA signature, combines information from nDNA fragments and organellar (mitochondrial, chloroplast, or plasmid) genomes. We demonstrate that, in this dataset, composite DNA signatures originating from two different organisms can be differentiated in all cases, including those where the use of CGR signatures of nDNA failed or was inconclusive. Another instance, the assembled DNA signature, combines information from many short DNA subfragments (e.g., 100 basepairs) of a given DNA fragment, to produce its signature. We show that an assembled DNA signature has the same distinguishing power as a conventionally computed CGR signature, while using shorter contiguous sequences and potentially less sequence information. CONCLUSIONS: Our results suggest that, while CGR signatures of nDNA cannot always play the role of genomic signatures, composite and assembled DNA signatures (separately or in combination) could potentially be used instead. Such additive signatures could be used, e.g., with raw unassembled next-generation sequencing (NGS) read data, when high-quality sequencing data is not available, or to complement information obtained by other methods of species identification or classification.

BACKGROUND: Motivated by the general need to identify and classify species based on molecular evidence, genome comparisons have been proposed that are based on measuring mostly Euclidean distances between Chaos Game Representation (CGR) patterns of genomic DNA sequences. RESULTS: We provide, on an extensive dataset and using several different distances, confirmation of the hypothesis that CGR patterns are preserved along a genomic DNA sequence, and are different for DNA sequences originating from genomes of different species. This finding lends support to the theory that CGRs of genomic sequences can act as graphic genomic signatures. In particular, we compare the CGR patterns of over five hundred different 150,000 bp genomic sequences spanning one complete chromosome from each of six organisms, representing all kingdoms of life: H. sapiens (Animalia; chromosome 21), S. cerevisiae (Fungi; chromosome 4), A. thaliana (Plantae; chromosome 1), P. falciparum (Protista; chromosome 14), E. coli (Bacteria - full genome), and P. furiosus (Archaea - full genome). To maximize the diversity within each species, we also analyze the interrelationships within a set of over five hundred 150,000 bp genomic sequences sampled from the entire aforementioned genomes. Lastly, we provide some preliminary evidence of this method's ability to classify genomic DNA sequences at lower taxonomic levels by comparing sequences sampled from the entire genome of H. sapiens (class Mammalia, order Primates) and of M. musculus (class Mammalia, order Rodentia), for a total length of approximately 174 million basepairs analyzed. We compute pairwise distances between CGRs of these genomic sequences using six different distances, and construct Molecular Distance Maps, which visualize all sequences as points in a two-dimensional or three-dimensional space, to simultaneously display their interrelationships. CONCLUSION: Our analysis confirms, for this dataset, that CGR patterns of DNA sequences from the same genome are in general quantitatively similar, while being different for DNA sequences from genomes of different species. Our assessment of the performance of the six distances analyzed uses three different quality measures and suggests that several distances outperform the Euclidean distance, which has so far been almost exclusively used for such studies.

We propose and investigate a formal language operation inspired by the naturally occurring phenomenon of DNA primer extension by a DNA-template-directed DNA Polymerase enzyme. Given two DNA strings u and v, where the shorter string v (called primer) is Watson-Crick complementary and can thus bind to a substring of the longer string u (called template) the result of the primer extension is a DNA string that is complementary to a suffix of the template which starts at the binding position of the primer. The operation of DNA primer extension can be abstracted as a binary operation on two formal languages: a template language L 1 and a primer language L 2 . We call this language operation L 1 -directed extension of L 2 and study the closure properties of various language classes, including the classes in the Chomsky hierarchy, under directed extension. Furthermore, we answer the question under what conditions can a given language of target strings be generated from a given template language when the primer language is unknown. We use the canonic inverse of directed extension in order to obtain the optimal solution (the minimal primer language) to this question.

Repetition avoidance has been intensely studied since Thue's work in the early 1900's. In this paper, we consider another type of repetition, called pseudopower, inspired by the Watson-Crick complementarity property of DNA sequences. A DNA single str

We investigate the role of nondeterminism in Winfree's abstract tile assembly model, which was conceived to model artificial molecular self-assembling systems constructed from DNA. By nondeterminism we do not mean a magical ability such as that possessed by a nondeterministic algorithm to search an exponential-size space in polynomial time. Rather, we study realistically implementable systems that retain a different sense of determinism in that they are guaranteed to produce a unique shape but are nondeterministic in that they do not guarantee which tile types will be placed where within the shape. We show a “molecular computability” result: there is an infinite shape S that is uniquely assembled by a tile system but not by any deterministic tile system. We show a “molecular complexity” result: there is a finite shape S that is uniquely assembled by a tile system with c tile types, but every deterministic tile system that uniquely assembles S has more than c tile types. In fact we extend the technique to derive a stronger (classical complexity theoretic) result, showing that the problem of finding the minimum number of tile types that uniquely assemble a given finite shape is ΣP2-complete. In contrast, the problem of finding the minimum number of deterministic tile types that uniquely assemble a shape is NP-complete [5].

In this paper, we introduce the notion of k-comma codes - a proper generalization of the notion of comma-free codes. For a given positive integer k, a k-comma code is a set L over an alphabet Σ with the property that LΣ k L ∩ Σ + LΣ + = ∅. Informally, in a k-comma code, no codeword can be a subword of the catenation of two other codewords separated by a “comma” of length k. A k-comma code is indeed a code, that is, any sequence of codewords is uniquely decipherable. We extend this notion to that of k-spacer codes, with commas of length less than or equal to a given k. We obtain several basic properties of k-comma codes and their generalizations, k-comma intercodes, and some relationships between the families of k-comma intercodes and other classical families of codes, such as infix codes and bifix codes. Moreover, we introduce the notion of n-k-comma intercodes, and obtain, for each k ≥ 0, several hierarchical relationships among the families of n-k-comma intercodes, as well as a characterization of the family of 1-k-comma intercodes.

Hairpin completion is an abstract operation modeling a DNA bio-operation which receives as input a DNA strand w = xαy\bar{α}, and outputs w' = xαy\bar{α}\bar{x}, where \bar{x} denotes the Watson-Crick complement of x. In this paper, we focus on the problem of finding conditions under which the iterated hairpin completion of a given word is regular. According to the numbers of words α and \bar{α} that initiate hairpin completion and how they are scattered, we classify the set of all words w. For some basic classes of words w containing small numbers of occurrences of α and \bar{α}, we prove that the iterated hairpin completion of w is regular. For other classes with higher numbers of occurrences of α and \bar{α}, we prove a necessary and sufficient condition for the iterated hairpin completion of a word in these classes to be regular.

Considering two DNA molecules which are Watson-Crick (WK) complementary to each other “equivalent” with respect to the information they encode enables us to extend the classical notions of repetition, period, and power. WK-complementarity has been modelled mathematically by an antimorphic involution θ, i.e., a function θ such that θ(xy) = θ(y)θ(x) for any x, y ∞ Σ*, and θ 2 is the identity. The WK-complementarity being thus modelled, any word which is a repetition of u and θ(u) such as uu, uθ(u)u, and uθ(u)θ(u)θ(u) can be regarded repetitive in this sense, and hence, called a θ-power of u. Taking the notion of θ-power into account, the Fine and Wilf’s theorem was extended as “given an antimorphic involution θ and words u, v, if a θ-power of u and a θ-power of v have a common prefix of length at least b(|u|, |v|) = 2|u| + |v| – gcd(|u|, |v|), then u and v are θ-powers of a same word.” In this paper, we obtain an improved bound b′(|u|, |v|) = b(|u|, |v|) – [gcd(|u|, |v|)/2]. Then we show all the cases when this bound is optimal by providing all the pairs of words (u, v) such that they are not θ-powers of a same word, but one can construct a θ-power of u and a θ-power of v whose maximal common prefix is of length equal to b′(|u|, |v|) − 1. Furthermore, we characterize such words in terms of Sturmian words.

Self-assembly, the process by which objects autonomously come together to form complex structures, is omnipresent in the physical world. Recent experiments in self-assembly demonstrate its potential for the parallel creation of a large number of nanostructures, including possibly computers. A systematic study of self-assembly as a mathematical process has been initiated by L. Adleman and E. Winfree. The individual components are modeled as square tiles on the infinite two-dimensional plane. Each side of a tile is covered by a specific “glue,” and two adjacent tiles will stick iff they have matching glues on their abutting edges. Tiles that stick to each other may form various two-dimensional “structures” such as squares and rectangles, or may cover the entire plane. In this paper we focus on a special type of structure, called a ribbon: a non-self-crossing rectilinear sequence of tiles on the plane, in which successive tiles are adjacent along an edge and abutting edges of consecutive tiles have matching glues. We prove that it is undecidable whether an arbitrary finite set of tiles with glues (infinite supply of each tile type available) can be used to assemble an infinite ribbon. While the problem can be proved undecidable using existing techniques if the ribbon is required to start with a given “seed” tile, our result settles the “unseeded” case, an open problem formerly known as the “unlimited infinite snake problem.” The proof is based on a construction, due to R. Robinson, of a special set of tiles that allow only aperiodic tilings of the plane. This construction is used to create a special set of directed tiles (tiles with arrows painted on the top) with the “strong plane-filling property”—a variation of the “plane-filling property” previously defined by J. Kari. A construction of “sandwich” tiles is then used in conjunction with this special tile set, to reduce the well-known undecidable tiling problem to the problem of the existence of an infinite directed zipper (a special kind of ribbon). A “motif” construction is then introduced that allows one tile system to simulate another by using geometry to represent glues. Using motifs, the infinite directed zipper problem is reduced to the infinite ribbon problem, proving the latter undecidable. An immediate consequence of our result is the undecidability of the existence of arbitrarily large structures self-assembled using tiles from a given tile set.

Self-assembly, the process by which objects autonomously come together to form complex structures, is omnipresent in the physical world. A systematic study of self-assembly as a mathematical process has been initiated. The individual components are modelled as square tiles on the infinite two-dimensional plane. Each side of a tile is covered by a specific "glue", and two adjacent tiles will stick if they have matching glues on their abutting edges. Tiles that stick to each other may form various two-dimensional "structures" such as squares, rectangles, or may cover the entire plane. In this paper we focus on a special type of structure, called ribbon: a non-self-crossing sequence of tiles on the plane, in which successive tiles are adjacent along an edge, and abutting edges of consecutive tiles have matching glues. We prove that it is undecidable whether an arbitrary finite set of tiles with glues (infinite supply of each tile type available) can be used to assemble an infinite ribbon. The proof is based on a construction, due to Robinson (1971), of a special set of tiles that allow only aperiodic tilings of the plane. This construction is used to create a special set of directed tiles (tiles with arrows painted on the top) with the "strong plane filling property" - a variation of the "plane filling property" previously defined by Kari (1990, 1994). A construction of "sandwich" tiles is then used in conjunction with this special tile set, to reduce the well-known undecidable tiling problem to the problem of the existence of an infinite directed zipper (a special kind of ribbon). A "motif" construction is then introduced that allows one tile system to simulate another by using geometry to represent glues. Using motifs, the infinite directed zipper problem is reduced to the infinite ribbon problem, proving the latter undecidable. The result settles an open problem formerly known as the "unlimited infinite snake problem". Moreover, an immediate consequence is the undecidability of the existence of arbitrarily large structures self-assembled using tiles from a given tile set.

The lower bounds on communication complexity measures of language generation by Parallel Communicating Grammar Systems (PCGS) are investigated. The first result shows that there exists a language that can be generated by some dag-PCGS (PCGS with communication structures realizable by directed acyclic graphs) consisting of 3 grammars, but by no PCGS with tree communication structure. The second result shows that dag-PCGS have their communication complexity of language generation either constant or linear.

We consider grammar systems in which several components are active at the same moment (a team of components is working). The power of such mechanisms is investigated and it is found that in many cases the team feature increases the generative capacity of grammar systems. In the so-called t-mode of derivation (a team works as much as it can) it is found that the team size does not induce an infinite hierarchy of languages. However, the family obtained in this case is a full abstract family of languages properly including ETOL.

The customary language-theoretic derivative of a word u with respect to a word v means the deletion of v from the beginning or end of u. We investigate the natural generalization, where v can be deleted from an arbitrary position in u. Apart from general closure and decidability properties, we pay special attention to regular languages, obtaining an exhaustive characterization.